Numerical model for eddy-current testing of ferromagnetic steel parts

Abstract

The paper presents an efficient numerical method to simulate eddy-current testing (ECT) of ferromagnetic steel parts. The method is based on the nonlinear integral equation for quasi-stationary electromagnetic field with gauge condition based on tree/cotree decomposition. The eddy-current density in the conductive domain and the magnetization in the ferromagnetic domain are discretized with edge elements and vectorial volume elements, respectively. A simple, but very effective magnetization model of steel in a low field is also presented. The algorithm convergence for solving the forward ECT nonlinear problem with time-periodic boundary conditions is proved.

Fast finite-element solver for a reluctance mass accelerator

“…By defining an initial material permeability and a maximum allowed magnetization , the hyperbolic tangent provides a reasonable saturation model, viz. (6) Note that there is no hysteresis provided in this model. There is nothing that prohibits the introduction of a hysteresis model (such as the Preisach model [14] or Jiles-Atherton Model [5], [15]) or other user-defined empirical models for .…”

“…The values of material magnetization and in (29) are computed from the th estimate for at each node within an element using the hyperbolic tangent expression in (6).…”

“…We then iterate around the inner loop which includes (29), (6) until changes in the vector potential vector, current, and voltage are less than the desired tolerance. It should be clear that the factorization of only needs to be computed once for each time step, thereby reducing the computational effort.…”

“…Here, instead of treating a reluctance "parameter" in the field equations and doing a traditional Newton-method linearization, we consider magnetic materials in the armature and sheath as contributing to the total field by means of their induced polarization density (or magnetization) (as is often done with integral-equation based field solvers [6], [7] and is used within the FEM framework by [8] and others for modeling permanent magnets). This approach permits a structuring of the discrete finite-element equations such that the nonlinear contribution from saturable materials is treated as a "source term" in the linearized set of equations.…”

Eddy Current Tomography for Nondestructive Testing

“…An alternative to the use of X-ray tomography can be eddy current tomography [3,4,5]. It allows for simultaneous measurement of magnetic susceptibility and resistivity of the material [6] in the tested element.…”